Residual Fourier-Padding Interpolation for Instrumentation and Measurement

1. A method of transforming an electronic analog signal into an interpolated, digital signal, comprising: (A) discretely sampling the electronic analog signal to produce a series of analog samples; (B) converting the series of analog samples into a series of digital samples representative of the series of analog samples; (C) constructing a mathematical model that approximately describes the series of digital samples; (D) subtracting the mathematical model from the series of digital samples, to yield a residue signal; (E) computing a DFT (Discrete Fourier Transform) of the residue signal; (F) zero-padding the DFT to yield a padded residue signal; (G) computing an inverse DFT of the padded residue signal to produce an interpolated residue signal; and (H) adding the interpolated residue signal to the mathematical model to produce the interpolated, digital signal.

2. A method as recited in claim 1 , wherein the step (B) of converting is performed by an analog-to-digital converter.

3. A method as recited in claim 1 , performed by an automatic test system under the direction of a test program for testing a unit under test, and further comprising using the interpolated, digital signal to determine whether the unit under test passes or fails the test program.

4. A method as recited in claim 1 , wherein the mathematical model represents large signal behavior of the sampled signal.

5. A method as recited in claim 1 , wherein the step of constructing the mathematical model comprises manually estimating the mathematical model.

6. A method as recited in claim 1 , wherein the step of constructing the mathematical model comprises analyzing the series of digital samples with a software program.

7. A method as recited in claim 1 , wherein the step of constructing the mathematical model comprises estimating the series of digital samples with one or more straight lines, parabolas, and/or polynomials.

8. A method of testing a UUT (Unit Under Test) in an ATE system, comprising: (A) connecting the UUT to an interface of an automatic test system; (B) electronically stimulating the UUT to produce an output signal; (C) sampling the output signal; (D) interpolating the sampled output signal; (E) comparing at least one signal characteristic of the interpolated sampled output signal with a predetermined test limit; and (F) indicating a passing or failing test result based upon the comparing step, wherein the step of interpolating the sampled output signal includes— constructing a mathematical model that approximately describes the sampled output signal subtracting the mathematical model from the sampled output signal, to yield a residue signal; computing a DFT (Discrete Fourier Transform) of the residue signal; zero-padding the DFT of the residue signal to yield a padded residue signal; computing an inverse DFT of the padded residue signal to produce an interpolated residue signal; and adding the interpolated residue signal to the mathematical model to produce the interpolated sampled output signal.

9. A method as recited in claim 8 , further comprising discarding or grading the UUT according to the passing or failing result.

10. A method as recited in claim 7 , wherein the at least one signal characteristic includes overshoot, undershoot, or slew rate.

11. A method as recited in claim 7 , wherein the mathematical model comprises one or more straight lines, parabolas, or polynomials.

12. A method of calibrating an instrument in an automatic test system, comprising: (A) exercising the instrument at each of a plurality of different frequencies; (B) measuring a response of the instrument at each of the plurality of frequencies to produce a sampled data set; (C) interpolating the sampled data set; and (D) adjusting the gain and/or phase of the instrument responsive to the interpolated data set, wherein the step of interpolating the sampled data set includes— constructing a mathematical model that approximately describes the sampled data set, subtracting the mathematical model from the sampled data set, to yield a residue; computing a DFT (Discrete Fourier Transform) of the residue; zero-padding the DFT of the residue to yield a padded residue; computing an inverse DFT of the padded residue to produce an interpolated residue; and adding the interpolated residue to the mathematical model to produce an interpolated version of the sampled data set.

13. A method as recited in claim 12 , wherein the instrument is a sourcing instrument.

14. A method as recited in claim 13 , wherein: the instrument is connected to the UUT at a test site; the step (A) of exercising comprises inducing the instrument to produce the plurality of different frequencies; and the step (B) of measuring comprises measuring at the test site.

15. A method as recited in claim 13 , wherein the sourcing instrument is one of a continuous wave frequency synthesizer and an arbitrary waveform generator.

16. A method as recited in claim 12 , wherein the instrument is a measuring instrument.

17. A method as recited in claim 16 , wherein: the instrument is connected to the UUT at a test site; the step (A) of exercising comprises applying signals to the instrument from the test site; and the step of (B) of measuring comprises inducing the instrument to make a measurement at each of the plurality of frequencies.

18. A method as recited in claim 17 , wherein the measuring instrument is a digitizer.

19. An apparatus for representing an electronic analog signal in digital form, comprising: means for sampling the electronic analog signal to produce a sampled signal; means for constructing a mathematical model that approximately describes the sampled signal; means for subtracting a mathematical model from the sampled signal, to yield a residue signal; means for computing a DFT (Discrete Fourier Transform) of the residue signal; means for zero-padding the DFT of the residue signal to yield a padded residue signal; means for computing an inverse DFT of the padded residue signal to produce an interpolated residue signal; and means for adding the interpolated residue signal to the mathematical model to produce an interpolated version of the sampled signal.

20. An apparatus for interpolating a data set, comprising: a modeling unit for storing a mathematical model that approximately describes the data set; a first summer having a first input for receiving the data set, a second input coupled to the modeling unit, and an output for providing a residue indicative of a difference between the sampled signal and the mathematical model; a DFT unit, coupled to the first summer, for computing a DFT (Discrete Fourier Transform) of the residue; a zero-padding unit, coupled to the DFT unit, for padding the DFT of the residue to yield a padded residue; an IDFT unit, coupled to the zero-padding unit, for computing an inverse DFT of the padded residue to produce an interpolated residue; and a second summer having a first input coupled to the IDFT unit, a second input coupled to the modeling unit, and an output for providing a sum of the interpolated residue and the mathematical model.